Lecture Discrete Mathematics given by Prof. Dr. Sebastian Iwanowski
study programs: Bachelor of Computer Science (B_Inf), Computer Engineering (B_Tinf), IT Engineering (B_ITE), Media Computer Science (B_Minf), Computer Games Technology (B_CGT), Business and Computer Science (B_Winf), e-Commerce (B_ECom), Smart Technology (B_STec), IT-Management Consulting & Auditing (B_IMCA), 1st semester
ECTS credits: 5
lecture term: summer and winter semester
prerequesites: precalculus mathematics of secondary school
language: This lecture is given in German in both semesters and in English in winter semester only.
schedule for WS 2016/17:
exercise + lecture: Tu, 11.00 hrs. - 14.00 hrs. including half an hour lunch break, HS 4
lecture: Th, 14.00 hrs. - 15.15 hrs., HS 1 (changed!)
focus of this lecture
This lecture gives the mathematical fundamentals for further study in all IT related programs. The contents are highly related to a lot of parallel and subsequent courses. This lecture does not require any knowledge of programming.
This lecture covers standard material such as logics and proof concepts, set theory, number theory, combinatorics, and graph theory. Furthermore, we give an introduction in group and field theory which highlights in the construction algorithm for arbitrary finite fields. For exercises, some construction programs implemented by students of FH Wedel in a software project may be downloaded here (instructions in German).
This lecture is complemented by exercises lead by teaching assistants.
content of teaching
The following links show the slides and the assignments of the course held in WS 2016/17. Students enrolled at FH Wedel will find all assignments and some student solutions on the handout server.
Assignment_1 (updated October 24, due October 27)
Assignment_2 (updated October 27, due November 1)
Assignment_3 (updated November 3, due November 8)
Assignment_4 (updated November 11, due November 15)
Assignment_5 (updated November 15, due November 22)
Assignment_6 (last updated November 29, due November 29)
4. Number theory
4.2 Dividing with remainders
4.3 Prime numbers
4.4 Modular arithmetic
(Examples for gcd and lcm, PrimeFactorisation with Maxima)
Note for the factorisation file: You must store this with the extension .wxm (not .txt). This file can the be executed and altered by the open-source tool Maxima (download here for all operating systems or here an older but still functioning version on the handout server for Windows). Warning: The file should not be altered by any editor other tha Maxima's!
Assignment_7 (last updated December 8, due December 6)
Assignment_8 (last updated December 8, due December 13)
5. Algebraic structures
Assignment_9 (last updated December 23, due December 20)
6.1 Enumeration formulae for sets
Assignment 10 (last updated December 23, due January 03)
7. Graph theory
7.1 Terminology und representation
7.2 Path problems in graphs (including Dijkstra's algorithm) (graph examples, algorithm example for Dijkstra)
7.3 Trees (including Kruskal's algorithm) (Ddodecaeder graph as an example for Kruskal (red) and Dijkstra (blue))
7.4 Planar graphs (Example for graph containing a subdivision of C3,3)
7.5 Graph colouring
Assignment 11 (last updated January 12, due January 10,12)
text book (in German)
Sebastian Iwanowski / Rainer Lang: Diskrete Mathematik mit Grundlagen, Springer 2014, ISBN 978-3-658-07130-1 (Print), 978-3-658-07131-8 (Online)
English books with partial coverage of this lecture (see slide references) or for further concentration:
Norman L. Biggs: Discrete Mathematics, Oxford University Press 2002 (2. edition), ISBN 0-19-850717-8
This book covers nearly all material of this lecture in a slightly more mathematical manner except for some graph algorithms. This book also covers a a lot of material not discussed in this lecture.
Neville Dean: The Essence of Discrete Mathematics, Prentice Hall 1997, ISBN 0-1334-5943-8
This book covers the first 2 chapters of this lecture entirely on a more elementary level.
Susanna S. Epp: Discrete Mathematics with Applications, Brooks/Cole 1995 (2. edition), ISBN 0-534-94446-9
This book covers most of this lecture (Chapter 5 not at all), some on a more elementary level, and lays a strong focus in algorithmic applications.
Jiri Matousek / Jaroslav Nesetril: An Invitation to Discrete Mathematics, Oxford University Press 2008 (2. edition), ISBN 0-1985-7042-2
This book covers some of the material of this lecture on a more scientific level and a lot of other issues for broadening the horizon.
Kenneth H. Rosen: Discrete Mathematics and its Applications, McGraw-Hill 2003, ISBN 0-07-242434-6
This book covers a big part of this lecture.
literature for broadening the mathematical horizon:
Martin Aigner / Günter Ziegler: Proofs from THE BOOK, Springer-Verlag 2010 (4. edition), ISBN 978-3-642-00855-9
Martin Aigner is my teacher of Discrete Mathematics.
In WS 2016, proofs of this book are presented in my seminar.